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Abstract

The Bhattacharyya, I-divergence, Vasershtein, variational and Levy distances are evaluated, compared and used for the reduction of n data to one feature. This reduction is obtained through a restricted linear transformation and the original data are assumed to be originating from two different jointly Gaussian classes. It is found that the Bhattacharyya, I-divergence and Vasershtein distances give the same "optimal" linear transformation that applied on the original n data result in one feature with maximum possible distance between classes. The distortion measures considered in the Vasershtein distance are |x-y| and (x-y)<sup>2</sup>. For the same distance measures and classes with equal covariances the Levy distance results in the same "optimal" linear transformation.